A mixing length model for turbulent flow in constant cross section ducts

1977 ◽  
Vol 10 (2) ◽  
pp. 125-129 ◽  
Author(s):  
R. P. Hornby ◽  
J. Mistry ◽  
H. Barrow
Keyword(s):  
Turbulent Flow ◽  
Cross Section ◽  
Constant Cross Section ◽  
Mixing Length

scholarly journals A study of the effect of curvature on fully developed turbulent flow

1935 ◽  
Vol 148 (865) ◽  
pp. 565-598 ◽  
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Boundary Layers ◽  
Cross Section ◽  
Variable Thickness ◽  
Curved Surfaces ◽  
Constant Cross Section ◽  
Curved Channel ◽  
Curved Boundary ◽  
Fully Developed Turbulent Flow

1—The solution of many important problems in aeronautics and hydraulics depends largely on the behaviour of turbulent flow along curved surfaces. In flow along plane surfaces the following method has proved to be successful. The laws of turbulent velocity distribution were investigated in straight tubes and channels of constant cross-section and the results applied to the boundary layer with variable thickness. The present work has undertaken with the idea of isolating the effect of curvature on the turbulent flow as much as possible, by using a curved channel of constant curvature and cross-section. It is hoped that the results of these experiments may be applied later to the general case of curved boundary layers.

Effects of openings on the seismic behavior and performance level of concrete shear walls

2019 ◽  
Author(s):  
Hossein Alimohammadi ◽  
Mostafa Dalvi Esfahani ◽  
Mohammadali Lotfollahi Yaghin
Keyword(s):  
Static Analysis ◽  
Cross Section ◽  
Seismic Behavior ◽  
Shear Walls ◽  
Shear Wall ◽  
Constant Cross Section ◽  
Added Resistance ◽  
Different Shapes ◽  
And Performance ◽  
Abaqus Software

In this study, the seismic behavior of the concrete shear wall considering the opening with different shapes and constant cross-section has been studied, and for this purpose, several shear walls are placed under the increasingly non-linear static analysis (Pushover). These case studies modeled in 3D Abaqus Software, and the results of the ductility coefficient, hardness, energy absorption, added resistance, the final shape, and the final resistance are compared to shear walls without opening.

Condensation in a Variable Acceleration Field and the Condensing Thermosyphon

1965 ◽  
Vol 87 (4) ◽  
pp. 355-360 ◽  
Author(s):  
J. C. Chato
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Radial Distance ◽  
Constant Cross Section ◽  
Linear Variation ◽  
Temperature Differential ◽  
Acceleration Field ◽  
Nusselt Numbers ◽  
Increasing Temperature ◽  
Limiting Values

The general problem of condensation in a variable acceleration field was investigated analytically. The case of the linear variation, which occurs in a constant cross section, rotating thermosyphon, was treated in detail. The results show that the condensate thickness and Nusselt numbers approach limiting values as the radial distance increases. The effects of the temperature differential and the Prandtl number are similar to those in other condensation problems; i.e., the heat transfer increases slightly with increasing temperature differential if Pr > 1, but it decreases with increasing temperature differential if Pr ≪ 1.

scholarly journals E–ε Model of Spray-Laden Near-Sea Atmospheric Layer in High Wind Conditions

2014 ◽  
Vol 44 (2) ◽  
pp. 742-763 ◽  
Author(s):  
Yevgenii Rastigejev ◽  
Sergey A. Suslov
Keyword(s):  
Turbulent Flow ◽  
Drag Coefficient ◽  
Turbulent Mixing ◽  
Numerical Solutions ◽  
Turbulent Energy ◽  
Wave Crest ◽  
Mixing Length ◽  
High Wind ◽  
Close Proximity ◽  
Ocean Spray

Abstract In-depth understanding and accurate modeling of the interaction between ocean spray and a turbulent flow under high wind conditions is essential for improving the intensity forecasts of hurricanes and severe storms. Here, the authors consider the E–ε closure for a turbulent flow model that accounts for the effects of the variation of turbulent energy and turbulent mixing length caused by spray stratification. The obtained analytical and numerical solutions show significant differences between the current E–ε model and the lower-order turbulent kinetic energy (TKE) model considered previously. It is shown that the reduction of turbulent energy and mixing length above the wave crest level, where the spray droplets are generated, that is not accounted for by the TKE model results in a significant suppression of turbulent mixing in this near-wave layer. In turn, suppression of turbulence causes an acceleration of flow and a reduction of the drag coefficient that is qualitatively consistent with field observations if spray is fine (even if its concentration is low) or if droplets are large but their concentration is sufficiently high. In the latter case, spray inertia may become important. This effect is subsequently examined. It is shown that spray inertia leads to the reduction of wind velocity in the close proximity of the wave surface relative to the reference logarithmic profile. However, at higher altitudes the suppression of flow turbulence by the spray still results in the wind acceleration and the reduction of the local drag coefficient.

Turbulent buoyant convection from a source in a confined region

1969 ◽  
Vol 37 (1) ◽  
pp. 51-80 ◽  
Author(s):  
W. D. Baines ◽  
J. S. Turner
Keyword(s):  
Point Source ◽  
Cross Section ◽  
Laboratory Experiments ◽  
Region Of Interest ◽  
Constant Cross Section ◽  
General Shape ◽  
Turbulent Environment ◽  
Starting Conditions ◽  
Upward Velocity ◽  
Local Mean

This paper considers the effect of continuous convection from small sources of buoyancy on the properties of the environment when the region of interest is bounded. The main assumptions are that the entrainment into the turbulent buoyant region is at a rate proportional to the local mean upward velocity, and that the buoyant elements spread out at the top of the region and become part of the non-turbulent environment at that level. Asymptotic solutions, valid at large times, are obtained for the cases of plumes from point and line sources and also periodically released thermals. These all have the properties that the environment is stably stratified, with the density profile fixed in shape, changing at a uniform rate in time at all levels, and everywhere descending (with ascending buoyant elements).The analysis is carried out in detail for the point source in an environment of constant cross-section. Laboratory experiments have been conducted for this case, and these verify the major predictions of the theory. It is then shown how the method can be extended to include more realistic starting conditions for the convection, and a general shape of bounded environment. Finally, the model is applied quantitatively to a variety of problems in engineering, the atmosphere and the ocean, and the limitations on its use are discussed.

scholarly journals A Case Study of Clear-Air Turbulence at Upper Levels

2021 ◽  
Author(s):  
Léo Rogel ◽  
Didier Ricard ◽  
Eric Bazile ◽  
Irina Sandu
Keyword(s):  
Turbulent Flow ◽  
Partial Information ◽  
Weather Prediction ◽  
Turbulent Fluxes ◽  
Small Scale ◽  
Mixing Length ◽  
Vertical Resolution ◽  
Stable Conditions ◽  
Study Results

<p>Because of the technical difficulties of achieving measurements at high altitudes, it is not clear how well turbulent phenomena are represented in the upper levels of current Numerical Weather Prediction (NWP) operational models.<br>Indeed, turbulence in strongly stable conditions near the tropopause is known to be particularly difficult to correctly parameterize. The constraining buoyancy forces on the vertical lead to anisotropic turbulence, potentially inhibiting turbulent production in NWP models.<br>Partial information for high altitude turbulence events is nonetheless available in the form of in-situ measurements from aircrafts. However, it only allows for qualitative comparisons with model outputs.<br>This study focuses on a turbulent episode induced by a winter upper-level jet above east Belgium on January 27, 2018, for which in-situ EDR (Eddy Dissipation Rate) reports indicate moderate-or-greater turbulence levels. Numerical simulations are performed with the Météo-France operational model AROME, and with the mesoscale research model MesoNH (Laero/CNRM), at the same horizontal grid resolution (1.3km). These two models also use the eddy-diffusivity turbulence scheme of Cuxart et al (2000), a 1.5 order closure scheme based on a prognostic Turbulent Kinetic Energy (TKE) evolution equation, with a diagnostic computation of the mixing length.<br>TKE budgets, as well as stability indices and gradient-based quantities (Richardson number, vertical wind shear) are computed from the model outputs, and qualitative comparison with in-situ data is presented. Time evolution of the turbulent event over Belgium is well captured by both models, agreeing with EDR data.<br>Several sensitivity tests on the vertical resolution, on the mixing length formulation and on the parameters of the TKE equation are then performed. Most notably, the use of an increased vertical resolution near the tropopause greatly enhances the turbulent fluxes in both operational and research models. Secondly, comparison of various expressions of the mixing length shows that the Bougeault and Lacarrere (1989) formulation produces the higher amount of subgrid TKE and turbulent mixing. A decreased turbulent dissipation parameter also significantly increases the amount of subgrid TKE. On the contrary, the use of a 3D turbulence scheme appears to have very limited impacts on the turbulent flow at this kilometer-scale horizontal resolution.<br>On a second part of this study, results from ongoing Large Eddy Simulations (LES) will be presented. These simulations aim at representing small-scale features of the turbulent flow. They will be used as a reference for the computation of turbulent fluxes at kilometer-scale resolution using a coarse-graining method, allowing for a comparison with the parameterized fluxes from the turbulence scheme. In particular, the dissipation term of the TKE equation will be examined. These results are expected to give insight on the leading turbulent mechanisms for which the current turbulence parameterization can be improved in stable conditions.</p>

Experimental study of particle-driven secondary flow in turbulent pipe flows

2012 ◽  
Vol 709 ◽  
pp. 1-36 ◽  
Author(s):  
R. J. Belt ◽  
A. C. L. M. Daalmans ◽  
L. M. Portela
Keyword(s):  
Turbulent Flow ◽  
Secondary Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Cross Section ◽  
Circular Pipe ◽  
Horizontal Pipe ◽  
Pipe Cross Section ◽  
Reynolds Stress Tensor ◽  
Pipe Flows

AbstractIn fully developed single-phase turbulent flow in straight pipes, it is known that mean motions can occur in the plane of the pipe cross-section, when the cross-section is non-circular, or when the wall roughness is non-uniform around the circumference of a circular pipe. This phenomenon is known as secondary flow of the second kind and is associated with the anisotropy in the Reynolds stress tensor in the pipe cross-section. In this work, we show, using careful laser Doppler anemometry experiments, that secondary flow of the second kind can also be promoted by a non-uniform non-axisymmetric particle-forcing, in a fully developed turbulent flow in a smooth circular pipe. In order to isolate the particle-forcing from other phenomena, and to prevent the occurrence of mean particle-forcing in the pipe cross-section, which could promote a different type of secondary flow (secondary flow of the first kind), we consider a simplified well-defined situation: a non-uniform distribution of particles, kept at fixed positions in the ‘bottom’ part of the pipe, mimicking, in a way, the particle or droplet distribution in horizontal pipe flows. Our results show that the particles modify the turbulence through ‘direct’ effects (associated with the wake of the particles) and ‘indirect’ effects (associated with the global balance of momentum and the turbulence dynamics). The resulting anisotropy in the Reynolds stress tensor is shown to promote four secondary flow cells in the pipe cross-section. We show that the secondary flow is determined by the projection of the Reynolds stress tensor onto the pipe cross-section. In particular, we show that the direction of the secondary flow is dictated by the gradients of the normal Reynolds stresses in the pipe cross-section, $\partial {\tau }_{rr} / \partial r$ and $\partial {\tau }_{\theta \theta } / \partial \theta $. Finally, a scaling law is proposed, showing that the particle-driven secondary flow scales with the root of the mean particle-forcing in the axial direction, allowing us to estimate the magnitude of the secondary flow.

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